`(a):\  (y)/(7)=(56)/(49)`

`(y)/(7)=(56:7)/(49:7)`

`(y)/(7)=(8)/(7)`

`y=8`

`(b):\   (15)/(27)=(5)/(y)\   (y\ne 0)`

`(15:3)/(27:3)=(5)/(y)`

`(5)/(9)=(5)/(y)`

`y=9` (Thỏa mãn)

`(c):\   (y-2)/(18)=(2)/(3)`

`(y-2)/(18)=(2xx6)/(3xx6)`

`(y-2)/(18)=(12)/(18)`

`y-2=12`

`y=12+2=14`

`(1):\  x^{2}-7x=0`

`<=>x(x-7)=0`

`=>x=0` hoặc `x-7=0`

`<=>x=0` hoặc `x=7`

`(2):\  -3x^{2}+5x=0`

`<=>3x^{2}-5x=0`

`<=>x(3x-5)=0`

`=>x=0` hoặc `3x-5=0`

`<=>x=0` hoặc `x=5/3`

`(3):\  x^{2}+3x-2x-6=0`

`<=>x(x+3)-2(x+3)=0`

`<=>(x+3)(x-2)=0`

`=>x+3=0` hoặc `x-2=0`

`<=>x=-3` hoặc `x=2`

`(c):\  (x-3)/(x+4)>0`

`=>`  \(\left[{}\begin{matrix}\left\{{}\begin{matrix}x-3>0\\x+4>0\end{matrix}\right.\\\left\{{}\begin{matrix}x-3< 0\\x+4< 0\end{matrix}\right.\end{matrix}\right.< =>\left[{}\begin{matrix}\left\{{}\begin{matrix}x>3\\x>-4\end{matrix}\right.\\\left\{{}\begin{matrix}x< 3\\x< -4\end{matrix}\right.\end{matrix}\right.\\ < =>\left[{}\begin{matrix}x>3\\x< -4\end{matrix}\right.\)

Vậy `S={x|x>3` hoặc `x< -4}`

`(a):\  (x-1)/(x+5)<0`

Do : `x+5>x-1` với mọi `x`

`=>` $\begin{cases}x-1<0\\x+5>0\end{cases}$

`<=>` $\begin{cases}x<1\\x> -5\end{cases}$

`<=>-5<x<1`

Vậy `S={x|-5<x<1}`

`(b):\  (x+2)/(x-5)<0`

Do : `x+2>x-5` với mọi `x`

`=>` $\begin{cases}x+2>0\\x-5<0\end{cases}$

`<=>` $\begin{cases}x> -2\\x<5\end{cases}$

`<=>-2<x<5`

Vậy `S={x|-2<x<5}`

`(14)/(9)xx(8)/(17)+(4)/(9)xx(8)/(17)`

`=(8)/(17)xx((14)/(9)+(4)/(9))`

`=(8)/(17)xx(18)/(9)`

`=(8)/(17)xx2`

`=(16)/(17)`

`\sqrt{x^{2}+4x+4}-2=1`

`<=>\sqrt{(x+2)^{2}}=3`

`<=>|x+2|=3`

`=>x+2=3` hoặc `x+2=-3`

`<=>x=1` hoặc `x=-5`

`(2x-15)^{5}=(2x-15)^{3}`

`=>(2x-15)^{5}-(2x-15)^{3}=0`

`=>(2x-15)^{3}[(2x-15)^{2}-1]=0`

`=>(2x-15)^{3}=0` hoặc `(2x-15)^{2}-1=0`

`=>2x-15=0` hoặc `2x-15=1` hoặc `2x-15=-1`

`=>x=15/2` hoặc `x=8` hoặc `x=7`

`P=(x+2)/(x\sqrt{x}-1)+(\sqrt{x}+1)/(x+\sqrt{x}+1)-(\sqrt{x}+1)/(x-1)`

`(ĐK:x\ge0;x\ne 1)`

`=(x+2)/(\sqrt{x}^{3}-1^{3})+(\sqrt{x}+1)/(x+\sqrt{x}+1)-(\sqrt{x}+1)/((\sqrt{x}-1)(\sqrt{x}+1))`

`=(x+2)/((\sqrt{x}-1)(x+\sqrt{x}+1))+(\sqrt{x}+1)/(x+\sqrt{x}+1)-(1)/(\sqrt{x}-1)`

`=(x+2+(\sqrt{x}+1)(\sqrt{x}-1)-(x+\sqrt{x}+1))/((\sqrt{x}-1)(x+\sqrt{x}+1))`

`=(x+2+x-1-x-\sqrt{x}-1)/((\sqrt{x}-1)(x+\sqrt{x}+1))`

`=(x-\sqrt{x})/((\sqrt{x}-1)(x+\sqrt{x}+1))`

`=(\sqrt{x}(\sqrt{x}-1))/((\sqrt{x}-1)(x+\sqrt{x}+1))`

`=(\sqrt{x})/(x+\sqrt{x}+1)`

`x^{2}+5xy+6y^{2}`

`=(x^{2}+2xy)+(3xy+6y^{2})`

`=x(x+2y)+3y(x+2y)`

`=(x+2y)(x+3y)`

`K=1+2^{2}+2^{4}+...+2^{98}+2^{100}`

`=>2^{2}.K=2^{2}+2^{4}+2^{6}+...+2^{100}+2^{102}`

`=>4K-K=(2^{2}+2^{4}+2^{6}+...+2^{100}+2^{102})-(1+2^{2}+2^{4}+...+2^{98}+2^{100})`

`=>3K=2^{102}-1`

`=>K=(2^{102}-1)/(3)`